Impervious; adjective; incapable of being influenced, persuaded, or affected.
From ” A Rose for Emily” pg 5, “Now and then we would see her in one of the downstairs windows– she had evidently shut up the top floor of the house– like the carven torso of an idol in a niche, looking or not looking at us, we could never tell which. Thus she passed from generation to generation– dear, inescapable, impervious, tranquil, and perverse.
After searching the word, I now understand that as the years passed, Miss Emily grew unaffected from any news or events that occurred in her life. She was in a sense, unsensible to any feelings or thoughts.
There are some more precise definitions of impervious that you should look at. The sense you get is only part of it, that information doesn’t seem to get through to her. But what else? Why do the townspeople care that she is impervious?